I'm happy it was helpful! A few more thoughts for the OP about this issue.
First, I wanted to plug Geoffrey Taucer's excellent video from his BHS clinic at Woodward. It provides a great explanation of the proper BHS shapes and drills.
Second, I am guessing that you may be working on BHS on beam given that you are doing a BT on floor. Since you want to undercut a beam BHS, it may be that practicing that has impacted your floor BHS. Maybe some other gymnasts or coaches could chime in with how to not let one affect the other.
Last, I thought of an analogy for what it should feel like when "falling back" during the takeoff of the BHS. This action gets the center of mass behind the feet and is essential to execute a long BHS (see above video). Have you ever had anyone play the trick where they pull your chair away but you catch yourself and instead of hitting the floor you pop up at the last second? Well, that is the feeling of a proper BHS takeoff. Right when you would pop up to not fall down, you instead jump back in a tight arch into your handstand.